The exponent for superalgebras with superinvolution

Let A be a superalgebra with superinvolution over a field of characteristic zero and let cn ⁎(A), n=1,2,… be its sequence of ⁎-codimensions. In [6] it was proved that such a sequence is exponentially bounded. In this paper we capture this exponential growth for finitely generated superalgebras with superinvolution A over an algebraically closed field of characteristic zero. We shall prove that limn→∞⁡cn ⁎(A)n exists and it is an integer, denoted exp⁎⁡(A) and called ⁎-exponent of A. Moreover, we shall characterize finitely generated superalgebras with superinvolution according to their ⁎-exponent.